On certain dense sets of rationals, simultaneous Schröder and Böttcher equations, and characterizations of functions

• Autores: A. Sklar
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 64, Nº. 3, 2002, págs. 232-247
• Idioma: inglés
• DOI: 10.1007/pl00012405
• Texto completo no disponible (Saber más ...)
• Resumen

  • The fact that rational numbers of the forms 2-m3n, m and n integers, are dense in the set \mathbbR+ of non-negative real numbers is crucial in determining well-behaved solutions of a key functional equation. A principal aim of this paper is the presentation of a new proof of the statement that many similar sets of rationals are dense in \mathbbR+ . The reason for giving a new proof of this statement is that the "standard" argument uses all the basic properties of logarithms and exponentials. The new proof does not, which means that our result can be used without circularity not only in the characterization, but in the very definition of logarithms and exponential functions.